Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
492 conjugacy classes of subgroups; only the 175 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 175 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C4×#13095512 | C2 | semidirect |
| 3. #20260848 | C2 | semidirect |
| 4. #20260846 | C2 | semidirect |
| 5. #20260842 | C2 | semidirect |
| 6. #20260838 | C2 | semidirect |
| 7. #20260833 | C2 | semidirect |
| 8. #20260770 | C2 | semidirect |
| 9. #20260730 | C2 | semidirect |
| 10. #97×D97 | C2 | semidirect |
| 11. #441×C97 | C2 | semidirect |
| 13. #15690833 | C4 | semidirect |
| 41. #13095512 | C2×C4 | semidirect |
| 49. #13095498 | C2×C4 | semidirect |
| 50. D776 | C2×C4 | semidirect |
| 54. C8×D97 | C2×C4 | semidirect |
| 65. Q16×C97 | C2×C4 | semidirect |
| 115. C97 | #2943 | semidirect |
| 121. #441 | D97 | semidirect |
| 165. Q16 | C4×D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690833 | 2 |
| C4×#13095512 | 2 |
| #20260848 | 2 |
| #20260846 | 2 |
| #20260842 | 2 |
| #20260838 | 2 |
| #20260833 | 2 |
| #20260770 | 2 |
| #20260730 | 2 |
| #97×D97 | 2 |
| #441×C97 | 2 |
| #2943 | 97 |